Selecting the length of a principal curve within a Gaussian model
نویسنده
چکیده
Principal curves are parameterized curves passing “through the middle” of a data cloud. These objects constitute a way of generalization of the notion of first principal component in Principal Component Analysis. Several definitions of principal curve have been proposed, one of which can be expressed as a least-square minimization problem. In the present paper, adopting this definition, we study a Gaussian model selection method for choosing the length of the principal curve, in order to avoid interpolation, and obtain a related oracle-type inequality. The proposed method is practically implemented and illustrated on cartography problems. Index terms – Principal curves, model selection, oracle inequality, slope heuristics. AMS 2010 Mathematics Subject Classification: 62G08, 62G05.
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